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Wave Optics

Question
CBSEENPH12040005

The electron in the hydrogen atom jumps from excited state (n=3) to its ground state (n=1) and the photons thus emitted irradiate a photosensitive material. If the work functions of the material is 5.1 eV, the stopping potential is estimated to be (the energy of the electron is nth state En = -13.6/n2 eV)

  • 5.1 V

  • 12.1 V

  • 17.2 V

  • 7 V

Solution

D.

7 V

For space straight n space equals space 1 comma space straight E subscript 1 space equals space minus space fraction numerator 13.6 over denominator left parenthesis 1 right parenthesis squared end fraction space equals space minus space 13.6 space eV
and space for space straight n space equals space 3 comma space straight E subscript 3 space equals space minus fraction numerator 13.6 over denominator left parenthesis 3 right parenthesis squared end fraction space equals space minus 1.51 space eV

so comma space required space energy space

straight E space equals space straight E subscript 3 minus space straight E subscript 1 space equals space minus space left parenthesis 1.51 right parenthesis minus space left parenthesis negative 13.6 right parenthesis
space equals space 12.09 space eV
straight E space equals space straight W space plus space eV
eV space equals space straight E minus space straight W
eV space equals space left parenthesis 12.09 minus 5.1 right parenthesis space straight e
straight V space equals space 7 space volt